Details

sample446.0ms

Algorithm

intervals

Results

275.0ms	111×	body	1280	valid
94.0ms	77×	body	640	valid
31.0ms	37×	body	320	valid
7.0ms	12×	body	160	valid
5.0ms	19×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune65.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

51.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
28.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

series371.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
209.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms	(cos (- lambda1 lambda2))
34.0ms	(sin (- lambda1 lambda2))

simplify3.6s

Counts

67 → 67

Iterations

Iter	Nodes
done	5020
3	2448
2	694
1	265
0	112

prune972.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.7b

localize161.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b	(cos (- lambda1 lambda2))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`cos-diff`
2×	`cos-sum` `associate-+r+` `sin-neg` `*-commutative` `distribute-rgt-neg-out`
1×	`+-commutative` `distribute-lft-neg-out` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

33.0ms	(* (cos lambda1) (sin (- lambda2)))
74.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
20.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))

series555.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (cos lambda1) (sin (- lambda2)))
198.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
207.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
37.0ms	(cos (- lambda1 lambda2))

simplify5.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5003
3	3897
2	968
1	330
0	135

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize135.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
8×	`associate-+r+`
7×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`neg-sub0` `cos-diff` `associate--l+`
3×	`sin-neg` `*-commutative` `distribute-rgt-neg-out`
2×	`sub-neg` `unswap-sqr`
1×	`+-commutative` `distribute-lft-neg-out` `flip3-+` `sum-log` `flip-+` `sin-mult`

Counts

4 → 77

Calls

4 calls:

36.0ms	(* (cos lambda1) (sin (- lambda2)))
34.0ms	(* (sin lambda1) (sin (- lambda2)))
73.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
19.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

series852.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (cos lambda1) (sin (- lambda2)))
107.0ms	(* (sin lambda1) (sin (- lambda2)))
172.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
479.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

simplify6.4s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	4885
2	1209
1	433
0	172

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize298.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1)))))
0.3b	(+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
0.7b	(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

380×	`associate-*r/`
244×	`frac-add` `cos-mult`
177×	`frac-times`
162×	`associate-*l/`
110×	`flip3-+` `flip-+`
107×	`sin-mult`
65×	`associate-/l/`
43×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate-/r/`
12×	`times-frac`
8×	`associate-+r+` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `cube-unmult` `pow3` `sum-cubes` `flip--`
4×	`pow-sqr` `pow-prod-up` `associate-/l*`
3×	`associate-/r*`
2×	`pow-plus` `associate--l+`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `frac-2neg` `diff-log` `swap-sqr` `div-exp` `associate-r` `associate-l` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 259

Calls

4 calls:

1.8s	(/ (+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1)))))
838.0ms	(+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))
308.0ms	(* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
84.0ms	(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series11.9s

Counts

4 → 12

Calls

4 calls:

8.4s	(/ (+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1)))))
2.7s	(+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))
337.0ms	(* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
411.0ms	(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify5.7s

Counts

271 → 271

Iterations

Iter	Nodes
done	5003
1	2483
0	727

prune6.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes1.8s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify24.0ms

Iterations

Iter	Nodes
done	69
1	69
0	47

end0.0ms

sample18.1s

Algorithm

intervals

Results

10.1s	3461×	body	1280	valid
5.9s	2422×	body	640	valid
1.0s	955×	body	320	valid
271.0ms	429×	body	160	valid
186.0ms	732×	body	80	valid
4.0ms	1×	body	2560	valid